Mastering Confidence Intervals

A confidence interval is a range of values, derived from sample statistics, which is likely to contain the value of an unknown population parameter. Its reliability is quantified by the confidence level.

The confidence level, typically expressed as a percentage (90%, 95%, 99%), indicates the probability that the interval will capture the true parameter value in repeated samples.

Margin of error is half the width of a confidence interval and reflects the extent of uncertainty or variability in the sample statistic.

A common misconception is that a 95% confidence interval contains the true parameter 95% of the time. Instead, 95% of such intervals from repeated sampling will contain the true parameter.

Confidence intervals are calculated using a point estimate from the sample, the standard error, and the z- or t-distribution depending on sample size and variance knowledge.

Unlike confidence intervals that estimate population parameters, prediction intervals predict the range for future individual observations and are generally wider.

Nonparametric methods like bootstrapping allow confidence interval construction without assuming a specific distribution, useful for complex or unknown distributions.